Topological charges in SL(2,R) covariant massive 11-dimensional and Type IIB SUGRA

TL;DR

This paper constructs explicit topological charge expressions for 1/2-BPS states in 10 and 11-dimensional supergravity, highlighting their SL(2,R) structure and implications for BPS spectrum analysis.

Contribution

It introduces new closed-form expressions for supergravity topological charges, extending the understanding of their multiplet structures and gauge transformations in SL(2,R) covariant frameworks.

Findings

Derived explicit topological charge expressions for BPS states.

Mapped charge multiplets between IIB and 11D supergravity.

Analyzed gauge transformations compatible with SL(2,R) covariance.

Abstract

In this paper we construct closed expressions that correspond to the topological charges of the various 1/2-BPS states of the maximal 10 and 11-dimensional supergravity theories. These expressions are related to the structure of the SUSY algebras in curved spacetimes. We mainly focus on IIB SUGRA and 11-dimensional SUGRA in a double M9-brane background, with an emphasis on the SL(2,R) multiplet structure of the charges and how these map between theories. This includes the charges corresponding to the multiplets of 7- and 9-branes in IIB. We find that examining the possible multiplet structures of the charges provides another tool for exploring the spectrum of BPS states that appear in these theories. As a prerequisite to constructing the charges we determine the field equations and multiplet structure of the 11-dimensional gauge potentials, extending previous results on the subject. The massive gauge transformations of the fields are also discussed. We also demonstrate how these massive gauge transformations are compatible with the construction of an SL(2,R) covariant kinetic term in the 11-dimensional Kaluza-Klein monopole worldvolume action.